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Chapter 5 The Performance of Feedback Control Systems

Chapter 5 The Performance of Feedback Control Systems. Test Input Signals Performance of a Second-Order System Effects of Third Pole and a Zero on the Second-Order System Response Estimation of the Damping Ratio The Steady-State Error of Feedback Control Systems Performance Indices.

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Chapter 5 The Performance of Feedback Control Systems

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  1. Chapter 5The Performance of Feedback Control Systems Test Input Signals Performance of a Second-Order System Effects of Third Pole and a Zero on the Second-Order System Response Estimation of the Damping Ratio The Steady-State Error of Feedback Control Systems Performance Indices

  2. Preview • The ability to adjust the transient and steady-state response of a feedback control system is a beneficial outcome of the design of control systems. • Input signals such as step and ramp are used to test the response of the control system. • In this chapter, common time-domain specifications are introduced: • Transient Response and Steady-State Response • Percent overshoot • Settling time • Time to peak • Time to Rise • Steady-State Tracking Error. • The concept of a performance index that represents a system’s performance by a single number (or index) will be considered..

  3. Test Input Signals

  4. Performance of a Second-Order System R(s) + E(s) Y(s)

  5. Standard Performance Measures

  6. The Steady-State Error of Feedback Control Systems Ea(s) G(s) K1 + Y(s) - H(s)

  7. Performance IndicesA performance index is a quantitative measure of the performance of a system and is chosen so that emphasis is given to the important system specifications.A system is considered an optimum control system when the system parameters are adjusted so that index reaches an extremum value, commonly a minimum value.A performance index, to be useful, must be a number that is always positive or zero

  8. Table 5.5 Summary of Steady-State Errors

  9. G(s) + E(s) Y(s) R(s) - H(s) E5.1: In order to get ess = 0; When the input is a step we require one integration (type 1 system). For a ramp input we require type 2 system.

  10. The Optimum Coefficients of T(s) Based on the ITAE Criterion for a Step Input

  11. 100/(s+2)(s+5) Y(s) R(s) E5.2: + -

  12. K / s(s+14) Y(s) R(s) E5.3 + -

  13. E5.8:

  14. G(s) + E(s) Y(s) R(s) - H(s) E5.10 The system is a type 1 (Table 5.5). The error constants are

  15. E5.13 GP(s) K/s(s+2) + E(s) Y(s) R(s) - K = 4 (s+3)/(s+0.1)

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